X-ray pulsar frequency dynamic estimation method based on chaos learning

Abstract

The invention discloses an X-ray pulsar frequency dynamic estimation method based on chaos learning, and belongs to the technical field of pulsar navigation, and the method comprises the steps: carrying out the SNE adaptive dimension reduction of a pulsar contour waterfall plot through the reconstruction of a high-dimensional space sample distance model, so as to meet the operation requirements of a satellite-borne industrial computer. A difference balance item is introduced into a cross entropy loss function, and the classification regression performance of the model is effectively improved by enhancing the distinction degree of net activity values of positive and negative sample output layers. According to a chaos phenomenon existing in a real neuron, a loss item based on chaos enhancement is designed and newly added. And the most suitable X-ray pulsar frequency is obtained after model screening. The method has the advantages of being suitable for navigating a pulsar source, high in estimation precision, high in estimation stability and the like, and the X-ray pulsar navigation performance can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of pulsar navigation, and particularly relates to a method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning. Background Art

[0002] As one of the core technologies of deep space exploration projects, autonomous navigation methods can improve the navigation accuracy and mission efficiency of spacecraft, reduce dependence on ground resources, and cope with unknown and complex environments. Among them, X-ray pulsar navigation, as a new type of astronomical ranging navigation, can provide high-precision spatio-temporal reference for spacecraft and has the ability to navigate over extremely long distances. It is currently an autonomous astronomical navigation method with great potential for spacecraft during the deep space exploration stage. When performing X-ray pulsar navigation, it is often necessary to combine ephemeris information to obtain the current frequency of the pulsar (because the frequency of the pulsar changes over time), and based on its frequency, restore the pulsar profile for the weak pulsar photons received by the detector to obtain a high-precision navigation measurement model. However, due to the "fault" phenomenon of pulsars, that is, the spin frequency and its derivative may undergo unpredictable mutations, this will cause the ephemeris information at this time to no longer be able to provide the accurate pulsar frequency, which may lead to the sudden failure of this navigation method. Therefore, directly using the photon information of pulsars received by the detector to perform real-time dynamic estimation of the current pulsar frequency can avoid the failure of the navigation method caused by pulsar "faults", so that X-ray pulsar navigation is applicable to any period of deep space exploration missions.

[0003] The existing dynamic estimation of pulsar frequency mainly focuses on statistical tests. The pulsar photons are folded and restored according to the candidate frequencies, and different test functions are used to perform significance tests on the folded pulsar profiles, so as to select the candidate frequency with the best test effect as the estimation result. Such methods are simple to calculate but are too sensitive to noise interference. In addition, with the further in-depth research on some pulsars, frequency estimation methods based on the matching of standard pulsar profiles have also been gradually applied. However, since the number of pulsars with known standard profiles is currently small, there are still certain limitations in using such methods for pulsar frequency estimation. At the same time, as an emerging method for visualizing pulsar profiles, the waterfall plot can also be used for the dynamic estimation of pulsar frequency. This method folds the pulsar photons in segments, not only paying attention to the significance of the folded waveforms of each segment, but also deeply excavating the photon information from the perspective of the consistency of the segmented folded waveforms. Such methods can make full use of pulsar photon information, but the calculation amount is large, posing a great challenge to on-board industrial computers. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning, which is a method for dynamically estimating the frequency of pulsars with higher estimation accuracy, more stable estimation effect, and stronger computing power, so as to further improve the performance of X-ray pulsar navigation; first, the pulsar profile waterfall diagram is adaptively reduced in dimension by Stochastic Neighbor Embedding (SNE) through reconstructing the high-dimensional space sample distance model, etc., to meet the computing requirements of on-board industrial computers. Secondly, a difference balance term is introduced into the cross-entropy loss function, and by enhancing the discrimination of the net activation values of the positive and negative sample output layers, the classification and regression performance of the model is effectively improved. Finally, to further improve the global search ability of the model, a loss term based on chaos enhancement is designed and added according to the chaotic phenomenon existing in real neurons; after model screening, the most suitable X-ray pulsar frequency is obtained. The present invention has the advantages of being applicable to navigation pulsar sources, high estimation accuracy, strong estimation stability, etc., and can effectively meet the accuracy requirements of X-ray pulsar navigation solution, thereby further improving the performance of X-ray pulsar navigation.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning, comprising the following steps:

[0007] Step 1: Perform SNE adaptive dimensionality reduction on the high-dimensional waterfall diagram of the pulsar profile by reconstructing the high-dimensional space sample distance model; SNE represents Stochastic Neighbor Embedding;

[0008] Step 2: Optimize the cross-entropy loss function, introduce a difference balance term for controlling the discrimination of the net activation values of the positive and negative samples in the output layer, and improve the regression prediction effect of the MLP model; MLP represents a multi-layer perceptron;

[0009] Step 3: Design and add a chaotic loss function based on the real neuron dynamics model to improve the global search ability of the MLP model and accelerate the training speed of the MLP model;

[0010] Step 4: Execute Steps 1 - 3 within all candidate periods, select the optimal SNE adaptive dimensionality reduction image through the MLP model, obtain the corresponding high-dimensional waterfall diagram based on the SNE adaptive dimensionality reduction image, and finally obtain the corresponding optimal X-ray pulsar frequency estimate.

[0011] Beneficial effects:

[0012] (1) The present invention performs SNE adaptive dimensionality reduction on the high-dimensional waterfall diagram of pulsar profiles by reconstructing the high-dimensional space sample distance model, etc., which can significantly improve the extraction effect of waterfall diagram features, reduce the calculation dimension and calculation cost at the same time, so as to meet the operation requirements of on-board industrial computers.

[0013] (2) The optimized cross-entropy loss function proposed by the present invention introduces a difference balance term that controls the discrimination degree of the net activation values of positive and negative samples in the output layer, and can reduce the network training deviation through artificial intervention, thereby improving the regression prediction accuracy of the model.

[0014] (3) By introducing a chaotic loss function based on the real neuron dynamics model, the present invention speeds up the convergence rate of the backpropagation algorithm, improves the adaptability of the model to perturbations, and enhances the stability and reliability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is a schematic diagram of the principle of a method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning according to the present invention;

[0016] Figure 2a Figure 2b Figure 2c are contour waterfall diagrams obtained by folding at different frequencies; among them, Figure 2a is the correct frequency-folded waterfall diagram, Figure 2b is the waterfall diagram with a certain error in frequency folding, Figure 2c is the waterfall diagram with completely wrong frequency folding;

[0017] Figure 3 are contour waterfall diagrams and SNE dimensionality reduction effect diagrams at different periods; from left to right, they represent the waterfall diagrams and SNE dimensionality reduction diagrams at periods P = 0.0337000000s, P = 0.0336999960s, P = 0.0336999920s, P = 0.0336999880s respectively. Among them, the upper diagrams are waterfall diagrams and the lower diagrams are SNE dimensionality reduction diagrams;

[0018] Figure 4 is a schematic diagram of the network balance optimization process based on the adjustment of the net activation value difference in the output layer;

[0019] Figure 5 is a schematic diagram of the update process of the weight gradient;

[0020] Figure 6 is a schematic diagram of the iterative process of the Kullback-Leibler (KL) divergence at different distances;

[0021] Figure 7SNE dimensionality reduction effect diagrams for different perplexities; the two leftmost diagrams represent waterfall diagrams for two periods of P = 0.0337000000 s and P = 0.0336999920 s respectively, and the three groups of diagrams on the right represent the dimensionality reduction effects of the SNE method when the perplexity is selected as 1, 40, and 200 respectively under the corresponding period P.

[0022] Figure 8 Box plot of the mean error of three estimation methods. Specific implementation manners

[0023] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the exemplary implementation manners of the present invention will be further described in detail below. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various implementation manners of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0024] As Figure 1 shown, the present invention proposes a method for dynamically estimating the frequency of X-ray pulsars by chaotic learning. First, the present invention performs SNE adaptive dimensionality reduction on the pulsar profile waterfall diagram by reconstructing the high-dimensional space sample distance model and other means to meet the computing requirements of the on-board industrial computer. Secondly, a difference balance term is introduced into the cross-entropy loss function. By enhancing the discrimination of the net activation values of the positive and negative sample output layers, the classification and regression performance of the model is effectively improved. Finally, to further improve the global search ability of the model, the present invention designs and adds a loss term based on chaos enhancement according to the chaotic phenomenon existing in real neurons; specifically, it includes the following steps:

[0025] Step 1: Use a detector to observe pulsar photons, perform data acquisition, and perform isochronous segmentation according to the total observation time to form a pulsar profile waterfall diagram, and perform SNE (Stochastic Neighbor Embedding) adaptive dimensionality reduction on the pulsar profile waterfall diagram (i.e., Figure 1 the SNE dimensionality reduction in

[0026] As Figure 2a , Figure 2b , Figure 2cAs shown, contour waterfall plot analysis has great potential in the accurate estimation of pulsar frequencies. However, the waterfall plot has a high computational complexity and low computational efficiency, which poses a certain challenge to the computing power of on-board industrial computers. Stochastic Neighbor Embedding (SNE) is an effective data dimensionality reduction method and an effective means to solve such problems. By mapping high-dimensional data points to a low-dimensional space, it reveals the internal structure of the data. However, due to problems such as a large number of hyperparameters and poor high-dimensional embedding effects, the results obtained by directly using the SNE method to reduce the dimensionality of the waterfall plot are often unsatisfactory. Therefore, it is necessary to adaptively improve the SNE method according to the characteristics of the pulsar contour waterfall plot to obtain better dimensionality reduction effects.

[0027] Due to its intuitive simplicity and relatively high computational efficiency, SNE often uses the Euclidean distance model as the high-dimensional sample distance model to measure the similarity of samples in the true dimension. However, since the contour waterfall plot increases the number of segments by reducing the number of photons in a single fold to achieve statistical analysis of the dimensionality-reduced data. Therefore, during a single fold process, the signal-to-noise ratio of the folded contour is usually low, which results in poor folding quality. At this time, if the Euclidean distance is still used to measure the similarity between high-dimensional samples, it may cause the measurement effect to deviate from the true situation due to the influence of noise. Based on this, the present invention introduces the cosine distance to reconstruct the high-dimensional space sample distance model. The cosine distance mainly measures the direction rather than the amplitude between each folded contour and is insensitive to amplitude noise. Secondly, the cosine distance can reduce the distance saturation effect in the high-dimensional space. All of these enable the cosine distance to more clearly reflect the similarity between contours when facing the contour waterfall plot.

[0028] (1)

[0029] Wherein, is the spatial distance between high-dimensional samples, is the th sample's spatial coordinate, is the number of samples.

[0030] Figure 3 shows the high-dimensional images obtained by folding the waterfall plot under 4 different candidate periods P and the distribution of 4 plane two-dimensional data points after SNE dimensionality reduction corresponding thereto. According to Figure 3 it can be found that performing SNE dimensionality reduction can not only retain the characteristics of the contour waterfall plot, but also effectively reduce the data dimensionality, laying a foundation for subsequent high-precision period estimation using the phase change characteristics of the folded contour. Figure 3Among them, from left to right, they respectively represent the waterfall plots and SNE dimensionality reduction plots at periods P = 0.0337000000 s, P = 0.0336999960 s, P = 0.0336999920 s, and P = 0.0336999880 s. Among them, the upper plot is the waterfall plot and the lower plot is the SNE dimensionality reduction plot.

[0031] Step 2: Introduce a difference balance term into the cross-entropy loss function to obtain a balanced cross-entropy loss function, so as to increase the distinguishability between positive and negative samples, thereby improving the regression prediction effect of the MLP model.

[0032] The dynamic estimation of pulsar frequency in the present invention essentially aims to use a multi-layer perceptron (MLP) model to solve the sorting problem in the regression task, that is, substituting candidate frequencies into the model and sorting them according to probability scores to select the optimal frequency. In such problems, "data imbalance" and "score overlap" are the key factors affecting the prediction effect. First, balance the number of positive and negative samples by undersampling "non-optimal" samples. Secondly, a balanced cross-entropy loss function based on the difference in the net activation values of the output layer is proposed to further distinguish positive and negative samples and improve the sorting accuracy.

[0033] Specifically, as Figure 4 shown, since some "non-optimal" samples are extremely similar to "optimal" samples, it may lead to the overlap of the net activation values of the output layer of positive and negative samples appearing, thus causing the sorting of the activated probability values to be reversed, directly affecting the estimation accuracy. Therefore, the cross-entropy loss function is optimized by introducing a balance term (difference balance term) based on the difference in the net activation values of the output layer. This part of the loss function, that is, the balanced cross-entropy loss function is designed as follows:

[0034] (2)

[0035] Among them, is the balanced cross-entropy loss function obtained from this calculation, is the difference balance term coefficient and is gradually reduced using the "annealing strategy", is the difference balance term, is the true label, is the model output value.

[0036] The main function of the difference balance term is to quantitatively consider whether the net activation values of the output layer of positive and negative samples overlap during loss calculation and gradient update, and to artificially intervene to separate them as much as possible to further reduce the problem of poor sorting effect caused by "score overlap". The specific design is the difference between the minimum net activation value of the positive sample output layer and the maximum net activation value of the negative sample output layer at the initial stage of network training, that is:

[0037] (3)

[0038] Among them, is the output net activation value of the neurons in the th layer, is the output net activation value of the negative samples of the neurons in the th layer, is the output net activation value of the positive samples of the neurons in the th layer, max represents the maximum value, and min represents the minimum value.

[0039] When performing weight and bias backpropagation, the gradients of the two can be expressed as:

[0040] (4)

[0041] (5)

[0042] Among them, is the weight of the neurons in the th layer, is the error term of the neurons in the th layer, is the activation value of the neurons in the th layer, is the bias term of the neurons in the th layer, and the superscript T represents the transpose of the matrix. is the number of neurons in the th layer.

[0043] Combined with formula (2), the error term of the output layer neurons of the MLP model of the present invention can be expressed as:

[0044] (6)

[0045] Among them, is the gradient of backpropagation of the neurons in the th layer, is the output activation value of the th layer and the th neuron, is the differential balance term coefficient, is the differential balance term, is the true label, is the model output value.

[0046] As can be seen from formula (6), the differential balance term proposed in the present invention directly participates in the gradient update process of the model weights and biases, that is, by introducing the difference in the net activation values of the positive and negative sample output layers, it affects the model parameter training process, enabling the model to pay more attention to the network training deviation caused by the "score overlap" problem during training, and adjusting the network parameters as much as possible to increase the distinguishability between positive and negative samples, thereby further improving the model regression prediction effect.

[0047] Step 3: Design and add a loss term based on chaos enhancement to enhance the global exploration ability and accelerate the convergence process;

[0048] By balancing and optimizing the cross-entropy loss function as described above, the model prediction accuracy can be significantly improved. However, the extremely similar features of some positive and negative samples still lead to weak gradient signals and stagnant weight updates, further exacerbating the problem of slow convergence speed of the backpropagation algorithm. This may be because the model training process ignores a key feature of neuron dynamics in the brain - chaos.

[0049] Chaos is a deterministic dynamic behavior with non-periodicity and non-linearity, and is extremely sensitive to the initial value. The traditional gradient descent method is often a local optimization process and is prone to falling into local minima. Introducing chaotic behavior can increase the exploration of the search space, help to more comprehensively discover the potential laws of data, and prevent the network from falling into overfitting or low-quality solutions. At the same time, chaotic behavior also helps to improve the network's adaptability to external perturbations, thereby enhancing the stability and reliability of the model.

[0050] Based on this, chaotic behavior is introduced into the gradient dynamics, and a chaos loss function with a high degree of dependence on state variables is designed and proposed :

[0051] (7)

[0052] where is the number of neuron layers of the MLP model, is the number of neurons in the th layer, is the chaos strength coefficient for controlling weight updates, is the rd th neuron's activation value in the

[0053] Combining formula (2) and formula (7), the dynamic model for weight gradient update can be obtained as:

[0054] (8)

[0055] where is the weight after neuron gradient update, is the learning rate, is the error term of the th layer and the th neuron. is the activation value of the th layer in the cross-entropy loss function. is the activation value of the th layer and the th neuron in the chaotic loss function. is the net activation value of the th layer and the th neuron in the chaotic loss function. can be embodied as the chaotic strong coefficient that controls the weight update. The superscript T represents the transpose of the matrix.

[0056] The update process of the weight gradient is as Figure 5 shown. The neural network includes an input layer, hidden layers, and an output layer. Figure 5 In it, k represents the kth neuron in this layer, and j represents the jth neuron in the previous layer. Equation (8) shows that the model weight update process is affected by the traditional gradient term and the chaotic term introduced in step 3, and it has a relatively clear biological meaning. First, the introduction of the chaotic term simulates the phenomenon that neurons in the brain use chaotic dynamics to avoid falling into local optimal solutions from gradient dynamics during learning. Second, the above gradient update model has a relatively consistent form with the neuron biological model proposed by Nagumo-Sato, and can more realistically approximate the neuron learning process. At the same time, this model simulates the critical state behavior of the brain. Specifically, the present invention adopts an annealing strategy for the chaotic strong coefficient . At the initial stage of network training, a stronger chaotic behavior is adopted to enhance the global exploration ability and accelerate the convergence process. As the network training progresses, the chaotic phenomenon is gradually reduced, and the training effect is stabilized in the traditional gradient update manner to achieve the mutual switching between traditional gradient learning and chaotic learning. In addition, the chaotic loss function adopts second-order state variable feedback, which can well reflect the high dependence of neuron state variables.

[0057] Step 4: Execute steps 1 - 3 within all candidate cycles, select the optimal SNE adaptive dimensionality reduction image through the MLP model, based on the cycle P corresponding to the SNE adaptive dimensionality reduction image, obtain the corresponding waterfall plot, and further inversely deduce the pulsar folding profile corresponding to the waterfall plot, and finally obtain the corresponding optimal X-ray pulsar frequency estimate.

[0058] Example:

[0059] The present invention selects to conduct research on the frequency dynamic estimation of the PSR B0531+21 pulsar. Due to the limited real dataset, the present invention uses a simulated generated dataset (4200 groups of positive and negative sample data each) for model training and experimental analysis.

[0060] Table 1 gives the KL divergence iteration convergence values under different numbers of partitions. As the number of partitions of photon events increases, the quality of the single-fold profile begins to decline. At this time, the cosine distance representation effect is significantly better than the Euclidean distance. At the same time, Figure 6 also gives the specific KL iteration change process of the two distance representation methods when the number of partitions of photon events is 200.

[0061] Table 1 KL convergence values of two distance representations under different numbers of partitions

[0062] It can be seen that when using the cosine distance to measure the similarity between high-dimensional samples, the KL divergence iteration convergence value is smaller, which means that the present invention using the cosine distance can obtain a low-dimensional representation closer to the distribution characteristics of high-dimensional samples and can achieve a better dimensionality reduction effect.

[0063] In addition, perplexity is one of the most important hyperparameters in the SNE method. It is a parameter measuring the local structure of data, which essentially controls the size of the local neighborhood and is usually described as an approximation of the number of neighbors perceived by each data point in high-dimensional data samples. The dimensionality reduction effects of SNE with different perplexities are as Figure 7 shown. The two leftmost figures represent waterfall diagrams under two periods of P = 0.0337000000s and P = 0.0336999920s respectively, and the three groups of figures on the right represent the dimensionality reduction effects of the SNE method when the perplexity is selected as 1, 40, and 200 respectively under the corresponding period P.

[0064] It can be seen that when the value of perplexity is appropriate, the dimensionality reduction effect is neither greatly affected by interference nor can it reflect the changes of subtle periods in a timely manner. Therefore, the perplexity is set to 40 in the present invention.

[0065] Finally, the training effect of the model is analyzed. First, the model finally formed by the present invention is compared and analyzed with other machine learning methods.

[0066] Table 2 Overall performance of the parameter indicators of each model in 10-fold cross-validation

[0067] As shown in Table 2, the generated dataset was subjected to 10-fold cross-validation using the above model. Among them, the precision rate of the support vector machine model was relatively low, while the recall rate was relatively high. This indicates that the model over-learned the positive samples, resulting in a possible overfitting phenomenon. The traditional MLP model also exhibited an imbalance between the precision rate and the recall rate, but the recall rate was relatively low. This indicates that the model did not learn the features sufficiently, possibly due to the loss function problem proposed above. The random forest model overcame the deficiencies of the first two models and was more effective in learning the data. However, its overall performance was still inferior to the MLP model of the present invention. The MLP model of the present invention was the most excellent in overall performance and had the highest accuracy rate. It not only prevented the overfitting phenomenon but also achieved sufficient learning of the features through the optimization of the loss function. Table 3 shows the specific performance of the MLP model of the present invention in the 10-fold cross-validation.

[0068] Table 3 Specific performance of the parameter indicators of the MLP model proposed by the present invention in the 10-fold cross-validation

[0069] To more intuitively demonstrate the performance effect of the model of the present invention, the model of the method of the present invention was compared with the traditional frequency estimation method based on test function and test function from the perspective of frequency estimation accuracy. According to the property that the estimated frequency and the estimated period are reciprocal to each other, the estimated period was used as the quantization evaluation index in the quantitative analysis of the present invention. The observation duration was set to 1000 s, the detector area was set to 1 m 2 , the search range was [0.0336999950 s, 0.0337000050 s], and the search step was 10 -10 s. At the same time, to ensure more stable estimation effects, multiple sub-MLP models based on undersampled negative samples were used for the comprehensive estimation of the optimal frequency. Hundreds of Monte Carlo experiments were conducted on the above three methods, and the period estimation error and the root mean square error (RMSE) are shown in Table 4 below. The box plots of the mean errors of the three estimation methods are as follows Figure 8 shown.

[0070] Table 4 Mean errors and RMSE of the three estimation methods

[0071] As can be seen from Table 4, under the same observation conditions, the method of the present invention was significantly superior to the traditional estimation method in terms of both the mean error and the RMSE. Especially compared with the test method that is more suitable for X-ray band frequency search, the mean error and the RMSE of our method were reduced by nearly half. This shows that the method of the present invention has relatively significant advantages in terms of estimation accuracy and estimation stability. At the same time, combined withFigure 8 The box plots of the three estimation methods can further verify that the method of the present invention has the smallest error distribution and interquartile range, and has the highest estimation accuracy and the most reliable estimation results among the three methods, indicating that the method of the present invention is more suitable for deep space exploration tasks with complex and variable detection conditions.

[0072] The specific embodiments described above further elaborate on the objectives, technical solutions and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning, characterized in that, It includes the following steps: Step 1: Perform SNE adaptive dimensionality reduction on the high-dimensional waterfall diagram of the pulsar profile by reconstructing the high-dimensional space sample distance model; SNE stands for Stochastic Neighbor Embedding; Step 2: Optimize the cross-entropy loss function, introduce a difference balance term to control the discrimination degree of the net activation values of positive and negative samples in the output layer, and improve the regression prediction effect of the MLP model; MLP stands for Multi-Layer Perceptron; Step 3: Design and add a chaotic loss function based on the real neuron dynamics model to enhance the global search ability of the MLP model and accelerate the training speed of the MLP model; Step 4: Execute Steps 1 - 3 within all candidate periods, select the optimal SNE adaptive dimensionality reduction image through the MLP model, obtain the corresponding high-dimensional waterfall diagram based on the SNE adaptive dimensionality reduction image, and finally obtain the corresponding optimal X-ray pulsar frequency estimation.

2. The X-ray pulsar frequency dynamic estimation method based on chaotic learning according to claim 1, characterized in that The said Step 1 includes: Introduce cosine distance to reconstruct the high-dimensional space sample distance model, so that SNE dimensionality reduction retains the characteristics of the profile waterfall diagram and effectively reduces the data dimensionality.

3. The method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning according to claim 2, wherein, The high-dimensional space sample distance model in the said Step 1 is: (1) Among them, is the spatial distance between high-dimensional samples, is the spatial coordinate of the th sample, and is the number of samples. It should be noted that in the original text, there seems to be an error in the repeated tag . The above translation is based on the overall understanding and correction of the text structure. If there are specific requirements for handling this repeated tag, it may need to be adjusted according to the actual situation.

4. A method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning according to claim 1, characterized in that, The said Step 2 includes: Firstly, balance the number of positive and negative samples by undersampling non-optimal samples; then propose a balanced cross-entropy loss function based on the difference of the net activation values in the output layer to further distinguish positive and negative samples and improve the ranking accuracy.

5. A method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning according to claim 4, characterized in that The said Step 2 includes: Balanced Cross-Entropy Loss Function Based on Output Layer Net Activity Value Difference is as follows: (2) Among them, is the differential balance term coefficient, is the differential balance term, is the true label, is the model output value.

6. The X-ray pulsar frequency dynamic estimation method based on chaotic learning according to claim 5, characterized in that The said Step 2 includes: Introduce a difference balance term that controls the discrimination degree of the net activation values of positive and negative samples in the output layer to affect the training process of the model parameters, enable the MLP model to consider the training deviation caused by the score overlap problem during training, and adjust the network parameters to increase the discrimination degree between positive and negative samples, further improving the regression prediction effect of the MLP model.

7. A method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning according to claim 6, characterized in that In the said Step 2, the error term of the neurons in the output layer of the MLP model is expressed as: (6) Among them, is the gradient of backpropagation of the layer of neurons, is the output activation value of the layer, the th neuron, is the number of neurons in the layer, represents the symbol for partial derivative.

8. A method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning according to claim 5, characterized in that The said Step 3 includes: Introduce chaotic behavior into gradient dynamics to obtain a chaotic loss function It is as follows: (7) Among them, is the number of neuron layers of the MLP model, is the number of neurons in the th layer, is the chaotic strong coefficient for controlling weight update, is the th in the th layer, and is the activity value of the th neuron.

9. A method for dynamically estimating the frequency of X-ray pulsars based on chaotic learning according to claim 8, characterized in that, The said Step 3 includes designing a dynamics model for weight gradient update, expressed as: (8) Among them, is the weight after neuron gradient update, is the learning rate, is the error term of the th neuron in the layer, is the activation value of the layer in the cross-entropy loss function, is the activation value of the th neuron in the layer in the chaotic loss function, is the activation value of the th neuron in the layer in the chaotic loss function, which is reflected as the chaotic strong coefficient controlling the weight update; the superscript T represents the transpose of the matrix.

10. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the said program, it realizes the steps of a method for dynamically estimating the X-ray pulsar frequency based on chaotic learning as described in any one of claims 1 to 9.

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